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13 votes
13 votes
Find the vertical asymptote(s) of f(x)=x2+3x+6/x2-4

User Elmiomar
by
3.1k points

1 Answer

10 votes
10 votes

Answer:

x=-2, 2

Explanation:

Aighty check this out


f(x) = \frac{ {x}^(2) + 3x + 6 }{ {x}^(2) - 4 } = = = > \\(x + 2)(x - 2) \\ so \: x = - 2 \: and \: x = 2 \: are \: not \: defined \: \\ and \: are \: the \: candidates

if non of the root give out 0/0 both can be the asymptotes:


f(2) = \frac{{2}^(2) + 3(2) + 6 }{ { - 2}^(2) + 4 } = = = > \\ f(2) = (16)/(0)

this one is OK


f( - 2) = \frac{ { - 2}^(2) + 3( - 2) + 6}{ { - 2}^(2) + 4 } = = = > \\ f( - 2) = (4)/(0)

so is this one

so the asymptotes are x=-2, 2

User Naptoon
by
2.2k points